Write the fraction in the simplest form:
`156/(108)`

Answer

To simplify the fraction \( \frac{156}{108} \), we will follow these steps:

### Step 1: Find the Greatest Common Divisor (GCD)
First, we need to find the GCD of the numerator (156) and the denominator (108). The GCD is the largest number that divides both numbers without leaving a remainder.

**Hint:** To find the GCD, you can list the factors of both numbers or use the prime factorization method.

### Step 2: Prime Factorization
Let's find the prime factorization of both numbers:

- For 156:
- Divide by 2: \( 156 \div 2 = 78 \)
- Divide by 2 again: \( 78 \div 2 = 39 \)
- Divide by 3: \( 39 \div 3 = 13 \)
- 13 is a prime number.

So, the prime factorization of 156 is \( 2^2 \times 3^1 \times 13^1 \).

- For 108:
- Divide by 2: \( 108 \div 2 = 54 \)
- Divide by 2 again: \( 54 \div 2 = 27 \)
- Divide by 3: \( 27 \div 3 = 9 \)
- Divide by 3 again: \( 9 \div 3 = 3 \)
- Divide by 3 again: \( 3 \div 3 = 1 \).

So, the prime factorization of 108 is \( 2^2 \times 3^3 \).

**Hint:** Write down the prime factors clearly to see which ones are common.

### Step 3: Identify Common Factors
From the prime factorizations:
- 156: \( 2^2 \times 3^1 \times 13^1 \)
- 108: \( 2^2 \times 3^3 \)

The common factors are \( 2^2 \) and \( 3^1 \).

### Step 4: Calculate the GCD
Now, multiply the lowest powers of the common prime factors:
- For \( 2 \): \( 2^2 = 4 \)
- For \( 3 \): \( 3^1 = 3 \)

So, the GCD is \( 4 \times 3 = 12 \).

**Hint:** The GCD helps us simplify the fraction.

### Step 5: Simplify the Fraction
Now, we can simplify the fraction by dividing both the numerator and the denominator by the GCD (12):

\[ \frac{156 \div 12}{108 \div 12} = \frac{13}{9} \]

### Final Answer
The simplest form of the fraction \( \frac{156}{108} \) is \( \frac{13}{9} \).

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